In the following figure,find m angle PBA. | vedclass

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(D) From the figure,$PA$ and $PB$ are tangents to the circle from an external point $P$. According to the theorem,the lengths of tangents drawn from a

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$55^{\circ}$

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(D) From the figure,$PA$ and $PB$ are tangents to the circle from an external point $P$. According to the theorem,the lengths of tangents drawn from an external point to a circle are equal,so $PA = PB$. In $	riangle PAB$,since $PA = PB$,it is an isosceles triangle. Therefore,the angles opposite to equal sides are equal,which means $m \angle PBA = m \angle PAB$. From the figure,the angle between the tangent $PA$ and the chord $AB$ is given as $55^{\circ}$. However,the angle $m \angle PAB$ is the angle between the tangent $PA$ and the chord $AB$. Thus,$m \angle PAB = 55^{\circ}$. Since $m \angle PBA = m \angle PAB$,we have $m \angle PBA = 55^{\circ}$.

In the following figure,find $m \angle PBA$.

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